Question

what is the product?
$3x^5\left(2x^2 + 4x + 1\
ight)$
\\(\circ\\) $2x^7 + 4x^6 + x^5$
\\(\circ\\) $6x^{10} + 12x^5 + 3x^5$
\\(\circ\\) $6x^7 + 12x^6 + 3x^5$
\\(\circ\\) $3x^5 + 2x^2 + 4x + 1$

Explanation:

Step1: Distribute $3x^5$ to each term

$3x^5 \cdot 2x^2 + 3x^5 \cdot 4x + 3x^5 \cdot 1$

Step2: Multiply coefficients and add exponents

$\frac{3 \cdot 2}{}x^{5+2} + \frac{3 \cdot 4}{}x^{5+1} + \frac{3 \cdot 1}{}x^{5}$

Step3: Simplify each term

$6x^7 + 12x^6 + 3x^5$

Answer:

C. $6x^7 + 12x^6 + 3x^5$